Problem: $K$ is the midpoint of $\overline{JL}$ $J$ $K$ $L$ If: $ JK = 8x + 8$ and $ KL = 5x + 35$ Find $JL$.
Solution: A midpoint divides a segment into two segments with equal lengths. ${JK} = {KL}$ Substitute in the expressions that were given for each length: $ {8x + 8} = {5x + 35}$ Solve for $x$ $ 3x = 27$ $ x = 9$ Substitute $9$ for $x$ in the expressions that were given for $JK$ and $KL$ $ JK = 8({9}) + 8$ $ KL = 5({9}) + 35$ $ JK = 72 + 8$ $ KL = 45 + 35$ $ JK = 80$ $ KL = 80$ To find the length $JL$ , add the lengths ${JK}$ and ${KL}$ $ JL = {JK} + {KL}$ $ JL = {80} + {80}$ $ JL = 160$